A general approximation result for nonlinear integral operators and applications to signal processing*

Abstract

Modular convergence theorems in Orlicz spaces for nets of nonlinear integral operators of the form where G and H are topological groups and {hw) is a family of homeomorphisms hwH→hw(H)CG are studied. The form of the above operators gives a unitary approach in order to obtain modular convergence theorems for several classical families of integral operators. In particular, in case of G = (R, +), H = (Z,+), hw(k) = k/w, Kw(z,.) = K(wz,.), we obtain modular convergence theorems in a classical Orlicz space for the nonlinear version of the generalized sampling series of f of the form: .